Geometric derivation of the polar equation of a cardioid, based on the geometric definition — the curve traced out by a point on a circle as the circle rolls around another circle of the same radius. #50famouscurves Tamás Görbe

New Modus Ponens just dropped: P→Q P ∴ P ∧Q Only a coward would merely conclude Q when P∧Q is stronger and more informative.

A geometric approach to explaining the horizontal shift when graphing transformed functions.

A problem from my calculus textbook, which takes either 5 seconds or 5 hours to solve. Join me on this journey to understand 🄸🄽🅃🄴🄶🅁🄰🄻🅂

Probability of returning to the origin in a random walk: 1D → P=1 2D → P=1 3D → P=0.34 Large D → P=1/2D

This got to be the scariest pumpkin I ever seen

Did you know the 2023 National Teacher of the Year is a MATH TEACHER? Better yet -- did you know she is speaking to MCPS staff on Nov 16? So excited to host you, Rebecka Peterson! Walter Johnson HS 3:00-4:00 November 16 Open to MCPS staff www2.montgomeryschoolsmd.org/news/bulletin/… #NTOY23 CCSSO

And did you know John Chase and I “met” through the math-teacher-internet world and have collaborated virtually for years! And now he’s invited me to his school home! I know the internet can bring out the worst in us. But sometimes…it brings out the best in us. #ntoy23 #oklaed

Some thoughts about Rolle's Theorem and the Mean Value Theorem. The theorems are most easily stated and most easily proved in their standard format, but their power comes from using the contrapositive.

Do you know what makes students think math is fun? When they understand it. We don’t have to make math fun…it already is. We just need to find better ways to help students learn it.

Anyone else going to MAA MathFest 2024 in Indianapolis? Hope to see you there! cvent.me/m08411?sms=2&c…

How to teach the Law of Cosines. First do a numeric example that reveals all the key relationships. Get a calculator and actually do it. Then effortlessly segue to the general case which generalizes the steps you just performed. That's it!

Comparing how fast the planets spin, and which way they point. Jupiter rips, Venus is a slowpoke! (great graphic by Dr. James O'Donoghue Dr James O'Donoghue!)

The NYC Math Festival is on until 4 pm today. Join MoMath for math games, exhibits, juggling, bubbles and more!

The 2024 ANNUAL NYC MATH FESTIVAL was a success! Thank you to the Tulipán Foundation, 28 Liberty, and the hundreds of passionate math enthusiasts of all ages who joined MoMath in celebrating the beauty and joy of mathematics this past Saturday.

So this is How to Teach. Meet students at the correct point on the Ladder of Abstraction, use a specific problem to prepare students to tackle the general case, prove the general case, then use this knowledge to subsequently solve other specific problems efficiently.

There's another way. It's a relatively minor tweak. Sometimes... just don't use the formulas. Show students how to live without them. Go back to 1. and just solve the problem from scratch like you did at the beginning. Be less efficient. Use actual mathematical reasoning.

We have to tear down this view of math learning that one thinks mathematically only in the acquisition of the formula and never again. Wake up that guy on the couch and get him back on the mountain! Only now the boulder is much smaller. With repetition, everything is easier.